What was already known
Martinsson and Steiner had established a constant-four scale for triangle-free d-degenerate graphs and conjectured the sharp leading constant one.
AI involvement
ChatGPT 5.5 Pro determined the optimized fractional clique function from an objective posed by Allen, Dhawan and Noel. They developed the construction, proof strategy and final article.
The model solved a central function-shape optimization, while the authors supplied the random construction and strategy.
Importance
The construction reaches the conjectured lower constant for arbitrarily large fixed girth.
Limitations
The authors designed the random construction and overall proof. Their separate upper-bound theorem is outside this AI assessment, and no completed check of the model’s optimization is documented.
Technical verification
A written proof and author responsibility are available, but no completed check of the model optimization is documented.
Human understanding
The authors explain the function and how it drives the lower-bound argument.
Correction and publication history
Only the model-assisted lower-bound function is assessed; the paper’s upper-bound proof is separate.
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